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        <p>二分搜索树</p>
<a id="more"></a>
<p>二叉树<br>一个节点最多有两个子节点<br>二×搜索树<br>如果一个二叉树满足：对于任意一个节点，其值不小于左子树的任何节点，且不大于右子树的任何节点（反之亦可），则为二×搜索树</p>
<p>对于set和get，以及remove方法而言，在二分搜索树中，是使用递归来处理的。先和根节点比较，如果相等，就不用继续执行操作了，如果比根节点小，就向左子树继续找下去；如果比根节点大，就向右子树找下去</p>
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class="line"></span><br><span class="line">    public BST()&#123;</span><br><span class="line">        root = null;</span><br><span class="line">        size = 0;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    public int size()&#123;</span><br><span class="line">        return size;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    public boolean isEmpty()&#123;</span><br><span class="line">        return size == 0;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 1.首先去看节点是否为空，如果为空，直接插入根节点的e中，否则就去和节点的元素e进行比较</span><br><span class="line">     * 2.如果和节点的元素相等，直接返回，不执行其他操作，</span><br><span class="line">     * 3.如果比节点e小，并且节点左子树为空，直接插入节点左子树</span><br><span class="line">     * 4.如果比节点eda，并且节点右子树为空，直接插入节点右子树</span><br><span class="line">     * 5.如果比节点e小，并且节点左子树不为空，那么就把现在的node和e，继续代入2，3，4，5，6</span><br><span class="line">     * 6.如果比节点e大，并且节点右子树不为空，那么就把现在的node和e，继续代入2，3，4，5，6</span><br><span class="line">     * @param e</span><br><span class="line">     */</span><br><span class="line">    public void addBase(E e)&#123;</span><br><span class="line">        if (root==null)&#123;</span><br><span class="line">            root=new Node(e);</span><br><span class="line">            size++;</span><br><span class="line">        &#125;else&#123;</span><br><span class="line">            addBase(root,e);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 添加元素</span><br><span class="line">     * @param node</span><br><span class="line">     * @param e</span><br><span class="line">     */</span><br><span class="line">    private void addBase(Node node,E e)&#123;</span><br><span class="line">        //与节点的元素进行比较，看是否相等，如果相等，就不继续执行下去，</span><br><span class="line">        if (e.equals(node.e))&#123;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">        //与节点的元素进行比较，看是否小于节点，</span><br><span class="line">        if (e.compareTo(node.e)&lt;0&amp;&amp;node.left==null)&#123;</span><br><span class="line">            node.left=new Node(e);</span><br><span class="line">            size++;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">        //与节点的元素进行比较，看是否大于节点，</span><br><span class="line">        if (e.compareTo(node.e)&gt;0&amp;&amp;node.left==null)&#123;</span><br><span class="line">            node.right=new Node(e);</span><br><span class="line">            size++;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">        if(e.compareTo(node.e) &lt; 0)&#123;</span><br><span class="line">            addBase(node.left, e);</span><br><span class="line">        &#125; else &#123;</span><br><span class="line">            addBase(node.right, e);</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 改进原版代码</span><br><span class="line">     * @param e</span><br><span class="line">     */</span><br><span class="line">    public void add(E e)&#123;</span><br><span class="line">            root=add(root,e);</span><br><span class="line">    &#125;</span><br><span class="line">    private Node add(Node node,E e)&#123;</span><br><span class="line">        //与节点的元素进行比较，看是否相等，如果相等，就不继续执行下去，</span><br><span class="line">        if (node==null)&#123;</span><br><span class="line">            size++;</span><br><span class="line">            return new Node(e);</span><br><span class="line">        &#125;</span><br><span class="line">        if(e.compareTo(node.e) &lt; 0)&#123;</span><br><span class="line">           node.left= add(node.left, e);</span><br><span class="line">        &#125; else if(e.compareTo(node.e) &gt; 0) &#123;</span><br><span class="line">            node.right=add(node.right, e);</span><br><span class="line">        &#125;</span><br><span class="line">        return node;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 元素e是否存在与树中</span><br><span class="line">     * @param e</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public boolean contains(E e)&#123;</span><br><span class="line">        boolean contains = contains(root, e);</span><br><span class="line">        return contains;</span><br><span class="line">    &#125;</span><br><span class="line">    public boolean contains(Node node,E e)&#123;</span><br><span class="line"></span><br><span class="line">        if (node==null)&#123;</span><br><span class="line">            return  false;</span><br><span class="line">        &#125;</span><br><span class="line">        if (e.compareTo(node.e) == 0)&#123;</span><br><span class="line">            return true;</span><br><span class="line">        &#125;</span><br><span class="line">        if(e.compareTo(node.e) &lt; 0)&#123;</span><br><span class="line">            return contains(node.left, e);</span><br><span class="line">        &#125;else&#123;</span><br><span class="line">            return contains(node.right, e);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 前序遍历</span><br><span class="line">     * 1）访问根节点</span><br><span class="line">     * 2）前序遍历左子树</span><br><span class="line">     * 3）前序遍历右子树</span><br><span class="line">     */</span><br><span class="line">    public  void preOrder()&#123;</span><br><span class="line">        preOrder(root);</span><br><span class="line">    &#125;</span><br><span class="line">    private void preOrder(Node node)&#123;</span><br><span class="line">        if (node==null)&#123;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">        System.out.println(node.e);</span><br><span class="line">        preOrder(node.left);</span><br><span class="line">        preOrder(node.right);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**中序遍历</span><br><span class="line">     *（1）中序遍历左子树</span><br><span class="line">     *（2）访问根节点</span><br><span class="line">     *（3）中序遍历右子树</span><br><span class="line">     */</span><br><span class="line">    public void inOrder()&#123;</span><br><span class="line">        inOrder(root);</span><br><span class="line">    &#125;</span><br><span class="line">    public void inOrder(Node node)&#123;</span><br><span class="line">        if (node==null)&#123;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">        preOrder(node.left);</span><br><span class="line">        System.out.println(node.e);</span><br><span class="line">        preOrder(node.right);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 后序遍历：</span><br><span class="line">     * （1）后序遍历左子树</span><br><span class="line">     * （2）后序遍历右子树</span><br><span class="line">     * （3）访问根节点</span><br><span class="line">     */</span><br><span class="line">    public void postOrder()&#123;</span><br><span class="line">        postOrder(root);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    private void postOrder(Node root) &#123;</span><br><span class="line">        if (root==null)&#123;</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line">        preOrder(root.left);</span><br><span class="line">        preOrder(root.right);</span><br><span class="line">        System.out.println(root.e);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 查找最小值</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public E minmum()&#123;</span><br><span class="line">        if (isEmpty())&#123;</span><br><span class="line">            throw new IllegalArgumentException(&quot;node is null&quot;);</span><br><span class="line">        &#125;</span><br><span class="line">        Node minmum = minmum(root);</span><br><span class="line">        return minmum.e;</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line">    private Node minmum(Node node)&#123;</span><br><span class="line">        if (node.left==null)&#123;</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        return minmum(node.left);</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 查找最大值</span><br><span class="line">     * @returnax</span><br><span class="line">     */</span><br><span class="line">    public E maxmum()&#123;</span><br><span class="line">        if (isEmpty())&#123;</span><br><span class="line">            throw new IllegalArgumentException(&quot;node is null&quot;);</span><br><span class="line">        &#125;</span><br><span class="line">        Node maxmum = maxmum(root);</span><br><span class="line">        return maxmum.e;</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line">    private Node maxmum(Node node)&#123;</span><br><span class="line">        if (node.right==null)&#123;</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        return maxmum(node.right);</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 删除链表的最小值</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public E removeMin()&#123;</span><br><span class="line">        E ret=minmum();</span><br><span class="line">        root=removeMin(root);</span><br><span class="line">        return ret;</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line">    private Node removeMin(Node node)&#123;</span><br><span class="line">        if (node.left==null)&#123;</span><br><span class="line">            node=node.right;</span><br><span class="line">            size--;</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        node.left = removeMin(node.left);</span><br><span class="line">        return node;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 删除链表的最max值</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public E removeMax()&#123;</span><br><span class="line">        E ret=minmum();</span><br><span class="line">        root=removeMax(root);</span><br><span class="line">        return ret;</span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line">    private Node removeMax(Node node)&#123;</span><br><span class="line">        if (node.right==null)&#123;</span><br><span class="line">            node=node.left;</span><br><span class="line">            size--;</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        node.right = removeMax(node.right);</span><br><span class="line">        return node;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 使用待删除元素的后继来完成删除操作</span><br><span class="line">     *</span><br><span class="line">     * @param e</span><br><span class="line">     */</span><br><span class="line">    public void remove(E e)&#123;</span><br><span class="line">        root=remove(root,e);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    private Node remove(Node node, E e) &#123;</span><br><span class="line">        if (node==null)&#123;</span><br><span class="line">            return null;</span><br><span class="line">        &#125;</span><br><span class="line">        if (node.e.compareTo(e)&lt;0)&#123;</span><br><span class="line">            node.left=remove(node.left,e);</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        if (node.e.compareTo(e)&gt;0)&#123;</span><br><span class="line">            node.right=remove(node.right,e);</span><br><span class="line">            return node;</span><br><span class="line">        &#125;else &#123;</span><br><span class="line">            if (node.left==null)&#123;</span><br><span class="line">                node=node.right;</span><br><span class="line">                size--;</span><br><span class="line">                return node;</span><br><span class="line">            &#125;</span><br><span class="line">            if (node.right==null)&#123;</span><br><span class="line">                node=node.left;</span><br><span class="line">                size--;</span><br><span class="line">                return node;</span><br><span class="line">            &#125;</span><br><span class="line"></span><br><span class="line">            Node minmum = minmum(node.right);</span><br><span class="line">            Node node1 = removeMin(node.right);</span><br><span class="line">            minmum.right=node1;</span><br><span class="line">            minmum.left=node.left;</span><br><span class="line">            node.left=node.right=null;</span><br><span class="line">            return minmum;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 使用前驱来进行数据的删除</span><br><span class="line">     * @param e</span><br><span class="line">     */</span><br><span class="line">    public void removePredecessor(E e)&#123;</span><br><span class="line">        root=removePredecessor(root,e);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    private Node removePredecessor(Node node, E e) &#123;</span><br><span class="line">        if (node==null)&#123;</span><br><span class="line">            return null;</span><br><span class="line">        &#125;</span><br><span class="line">        if (node.e.compareTo(e)&lt;0)&#123;</span><br><span class="line">            node.left=removePredecessor(node.left,e);</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        if (node.e.compareTo(e)&gt;0)&#123;</span><br><span class="line">            node.right=removePredecessor(node.right,e);</span><br><span class="line">            return node;</span><br><span class="line">        &#125;</span><br><span class="line">        else&#123;</span><br><span class="line">            if (node.left==null)&#123;</span><br><span class="line">                node=node.right;</span><br><span class="line">                size--;</span><br><span class="line">                return node;</span><br><span class="line">            &#125;</span><br><span class="line">            if (node.right==null)&#123;</span><br><span class="line">                node=node.left;</span><br><span class="line">                size--;</span><br><span class="line">                return node;</span><br><span class="line">            &#125;</span><br><span class="line">            Node maxmum = maxmum(node.right);</span><br><span class="line">            Node node1 = removeMax(node.right);</span><br><span class="line">            maxmum.right=node1;</span><br><span class="line">            maxmum.left=node.left;</span><br><span class="line">            node.left=node.right=null;</span><br><span class="line">            return maxmum;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    @Override</span><br><span class="line">    public String toString()&#123;</span><br><span class="line">        StringBuilder res = new StringBuilder();</span><br><span class="line">        generateBSTString(root, 0, res);</span><br><span class="line">        return res.toString();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 生成以node为根节点，深度为depth的描述二叉树的字符串</span><br><span class="line">      */</span><br><span class="line">    private void generateBSTString(Node node, int depth, StringBuilder res)&#123;</span><br><span class="line"></span><br><span class="line">        if(node == null)&#123;</span><br><span class="line">            res.append(generateDepthString(depth) );</span><br><span class="line">            return;</span><br><span class="line">        &#125;</span><br><span class="line"></span><br><span class="line">        res.append(generateDepthString(depth) + node.e +&quot;\n&quot;);</span><br><span class="line">        generateBSTString(node.left, depth + 1, res);</span><br><span class="line">        generateBSTString(node.right, depth + 1, res);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    private String generateDepthString(int depth)&#123;</span><br><span class="line">        StringBuilder res = new StringBuilder();</span><br><span class="line">        return res.toString();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

      
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